Chebyshev Wavelets

Abstract

In this note we introduce a new family of wavelets, named Chebyshev wavelets, which are derived from conventional Chebyshev polynomials. Properties of Chebyshev filter banks are investigated, including orthogonality and perfect reconstruction conditions. Chebyshev wavelets of 2nd kind have compact support, their filters possess good selectivity, but they are not orthogonal. The convergence into 2nd kind Chebyshev wavelets via the cascade algorithm is proved by the use of Markov chains theorems. Computational implementation of these wavelets and some clear-cut applications are presented. These wavelets are offered as a choice in wavelet analysis. Keywords— Wavelets, Filter banks, Chebyshev polynomials, Wavelet design.